Verify the following are identities by taking a, b, c as positive inte

1.	Verify the following are identities by taking a, b, c as positive integers. (i) (a – b)2 = a2 – 2ab + b2(ii) (a + b) (a – b) = a2 – b2
Answer» i) (a – b)² = a² – 2ab + b² a = 3, b = 1 ⇒ (3 – 1)² = (3)² – 2 × 3 × 1 + 1² ⇒ (2)² = 9 – 6 + 1 ⇒ 4 = 4 ∴ (i) is an identity, ii) (a + b) (a – b) = a² – b² a = 2, b = 1 ⇒ (2 + 1) (2 – 1) = (2)² – (1)² ⇒ 3 × 1 = 4 – 1 ⇒ 3 = 3 ∴ (ii) is an identity.

Verify the following are identities by taking a, b, c as positive integers. (i) (a – b)2 = a2 – 2ab + b2(ii) (a + b) (a – b) = a2 – b2

Answer»

i) (a – b)² = a² – 2ab + b²

a = 3, b = 1

⇒ (3 – 1)² = (3)² – 2 × 3 × 1 + 1²

⇒ (2)² = 9 – 6 + 1

⇒ 4 = 4

∴ (i) is an identity,

ii) (a + b) (a – b) = a² – b²

a = 2, b = 1

⇒ (2 + 1) (2 – 1) = (2)² – (1)²

⇒ 3 × 1 = 4 – 1

⇒ 3 = 3

∴ (ii) is an identity.